Overcoming the Limitations of Latent Gaussian Models: A Systematic Review of INLA-based Hybrid Machine Learning

The increasing demand for accurate inference and forecasting has driven the search for models capable of capturing complex spatio-temporal dynamics. This systematic literature review aims to provide a comprehensive synthesis of hybrid approaches that combine the Integrated Nested Laplace Approximation (INLA) with machine learning methods. Specifically, the review encompasses tree-based nonparametric models integrated with INLA and hybrid architectures that employ neural networks within the INLA framework. The central objective is to examine how INLA, a powerful and revolutionary tool for handling spatio-temporal data, can be enhanced by using it within a framework that simultaneously and integrally leverages machine learning methodologies. By identifying the strengths and limitations of these hybrid approaches, this review seeks to clarify the current state of the art and establish a foundation for developing models that effectively and simultaneously exploit the treatment of uncertainty connected to Bayesian inference with the flexibility and predictive power of machine learning.